Compensation of Modal Dispersion in Multimode Fiber Systems

Compensation of Modal Dispersion in Multimode Fiber Systems using Adaptive Optics via Convex Optimization Rahul Alex Panicker Department of Electrical Engineering Stanford Univeristy

Playing an Electromagnetic F Major on an Optical Fiber

Multimode Fiber Systems – what, why? l Ubiquitous short range communication medium 3

Multimode Fiber Systems – what, why? l l Ubiquitous short range communication medium Local area networks, campus area networks 4

Multimode Fiber Systems – what, why? l l l Ubiquitous short range communication medium Local area networks, campus area networks Lots of installed fiber – can we make the best use of this? (remember telephone lines and DSL? ) 5

Multimode Fiber Systems – what, why? Ethernet Roadmap 6

Multimode Fiber Systems – what, why? Performance – bit rate (Mbps/Gbps) and transmission distance (km) – currently limited by modal dispersion. 7

Contributions of this Thesis l l l Adaptive transmission scheme involving optical dispersion compensation. New comprehensive mathematical formulation. Performance maximization posed as an optimization problem. Globally optimal solution computed. Created novel adaptive algorithms for real-time implementation. Experimental demonstration of 10 Gbps and 100 Gbps transmissions. 8

Outline Multimode fiber essentials l Adaptive transmission scheme l Optimization problem l Adaptive algorithms l Experimental results l 9

Outline Multimode fiber essentials l Adaptive transmission scheme l Optimization problem l Adaptive algorithms l Experimental results l 10

Modes of a Multimode Fiber l Many natural phenomena involve modes: Solar oscillations l Swaying buildings l Vibrating strings l Ripples in a pond l Molecular vibrations l Light in an optical fiber l 11

Modes of a Multimode Fiber And God said… …and then there was light. 12

Modes of a Multimode Fiber Ideal Modes l l l Mutually orthogonal solutions of wave equation having well-defined propagation constants. Propagate without cross-coupling in ideal fiber. Typical multimode fiber supports of order 100 modes. 13

Modes of a Multimode Fiber Mode Coupling l l Bends and imperfections couple modes over distances of the order of meters. Coupling varies on time scale of seconds. 14

Modes of a Multimode Fiber Modal Dispersion l l Different modes have different delays. Single pulse in – many pulses out. Received Transmitted t t 15

Modes of a Multimode Fiber Principal modes l PMs are linear combinations of ideal modes. l Form a basis over all propagating modes. l Vary from fiber to fiber. Single pulse in – single pulse out (well defined group delay). l S. Fan and J. M. Kahn, Optics Letters, vol. 30, no. 2, pp. 135 -137, January 15, 2005. 16

Eye Diagram Indicates how discernable 1 -bits and 0 -bits are. Goodeye Bad Poor eye 17

Outline Multimode fiber essentials l Adaptive transmission scheme l Optimization problem l Adaptive algorithms l Experimental results l 18

Adaptive Transmission Scheme Fourier Lens Iout(t) Adaptive Algorithm Multimode Fiber Spatial Light Modulator Trans. Data Photo. Detector Iin(t) Clock & Data Recovery Rec. Data ISI Estimation OOK Modulator Transmitter Receiver ISI Objective Function Low-Rate Feedback Channel +0. 1 E. Alon, V. Stojanovic, J. M. Kahn, S. P. Boyd and M. A. Horowitz, Proc. of IEEE Global Telecommun. Conf. , Dallas, TX, Nov. 29 -Dec. 3, 2004. 19

Spatial Light Modulator ky y kx x MMF SLM l l 2 -D array of mirrors. Reflectance each mirror (vi) can be controlled. 20

Adaptive Transmission Scheme Fourier Lens Iout(t) Adaptive Algorithm Multimode Fiber Spatial Light Modulator Trans. Data Photo. Detector Iin(t) Clock & Data Recovery Rec. Data ISI Estimation OOK Modulator Transmitter Receiver ISI Objective Function Low-Rate Feedback Channel +0. 1 -0. 3 +0. 8 +0. 4 21

Outline Multimode fiber essentials l Adaptive transmission scheme l Optimization problem l Adaptive algorithms l Experimental results l 22

Optimization Problem maximize eye opening subject to physical constraints 23

Optimization Problem The impulse response is given by The pulse response is, therefore, given by and the eye opening is given by 24

Optimization Problem l l Not in any standard form. For example, not convex. R. A. Panicker, S. P. Boyd, and J. M. Kahn, subm. Journal of Lightwave Technology 25

Optimization Problem l Convex! (Second order cone program) 26

Optimization Problem l l l Can compute globally optimal solution. Efficient algorithms exist. Roughly same complexity as solving a linear program of same size. 27

Simulation Results 28

Outline Multimode fiber essentials l Adaptive transmission scheme l Optimization problem l Adaptive algorithms l Experimental results l 29

Adaptive Algorithms l l l Optimal solution – fine when everything is known about the system. In practice, we don’t know system parameters. System can be time varying. Need adaptive algorithms. Can compute optimum without explicitly estimating system parameters. 30

Adaptive Algorithms: Noiseless Amplitude-and-Phase SCA (APSCA): 1) 2) 3) 4) Pick the ith SLM block Optimize amplitude and phase of vi i ← i+1 Repeat 31

Adaptive Algorithms: Noiseless l l Quadratic in each block reflectance. 4 real parameters to be estimated in a, b, and c. Can be done with 4 measurements. Objective function converges to global maximum. (on convergence, satisfies KKT conditions of convex problem) 32

Adaptive Algorithms: Noiseless Continuous Phase SCA (CPSCA): 1) 2) 3) 4) Pick the ith SLM block Optimize phase of vi i ← i+1 Repeat 33

Adaptive Algorithms: Noiseless l l Linear in each block reflectance. 3 real parameters to be estimated in b and d. Can be done with 3 measurements. Guaranteed to converge, but not to global optimum. 34

Simulations Amplitude-and-Phase SCA: Opens a previously closed eye. 35

Simulations 36

Simulations Amplitude-and-Phase SCA, Continuous-Phase SCA, and 4 -Phase SCA 0. 6 Global maximum Normalized objective function 0. 4 0. 2 0 1 pass over SLM CPSCA 1 pass over SLM APSCA, 4 PSCA -0. 2 -0. 4 APSCA CPSCA 4 PSCA -0. 6 -0. 8 0 100 200 300 400 500 600 Number of SLM block flips 700 37

Adaptive Algorithms: Noisy Amplitude-and-Phase SCA (APSCA): 1) 2) 3) 4) 5) Pick the ith SLM block Estimate a, b, c. Optimize amplitude and phase of vi i ← i+1 Repeat 38

Adaptive Algorithms: Noisy Estimation done with p+q measurements, p ≥ 3, q ≥ 1. If noise has variance σ2, var(a) = σ2(1/p+1/q), var(Re(b)) = var(Im(b)) = σ2/p. In presence of Gaussian noise, these are ML estimates. 39

Adaptive Algorithms: Noisy Continuous Phase SCA (CPSCA): 1) 2) 3) 4) 5) Pick the ith SLM block Estimate b and d. Optimize phase of vi i ← i+1 Repeat 40

Adaptive Algorithms: Noisy Estimation done with p measurements, p ≥ 3. If noise has variance σ2, var(Re(b)) = var(Im(b)) = σ2/p. In presence of Gaussian noise, these are ML estimates. 41

Simulations Convergence Plots: Amplitude-and-Phase SCA, Continuous-Phase SCA, and 4 -Phase SCA Global maximum 0. 4 Objective function 0. 2 0 -0. 2 1 pass over SLM APSCA without noise APSCA with noise CPSCA with noise 4 PSCA with noise -0. 4 -0. 6 -0. 8 0 100 200 300 400 Number of SLM block flips 500 42

Adaptation Time l Presently, 3– 4 minutes in lab setup. l Objective function estimation time can be reduced to 25 ms l SLM switching time can be reduced to 100 ms l Overall adaptation (60 blocks, 4 phases) would require 30 ms 43

Comparison with Electrical Equalization l l l Optimal equalizer is MLSD – complexity exponential in bit-rate and length. Linear equalizers have noise enhancement. DFE has error propagation at low SNR. EE needs to be done per channel in WDM systems. Steady power consumption 44

Comparison with Electrical Equalization Optical Equalization l l Complexity independent of bit-rate and length – only depends on mode structure. No noise enhancement. Can compensate over multiple channels in WDM systems. After adaptation, no steady power consumption. 45

Outline Multimode fiber essentials l Adaptive transmission scheme l Optimization problem l Adaptive algorithms l Experimental results l 46

Transmission Scheme X. Shen, J. M. Kahn and M. A. Horowitz, Optics Letters, vol. 30, no. 22, pp. 2985 -2987, Nov. 15, 2005. 47

Transmission Scheme 48

Estimation of the Objective Function g(t) g(n. T; t 0) 0 T 2 T 3 T 4 T 5 T 6 T t - t 0 Eye closed: transmit periodic square wave Receive y(t) = Iout(t) * r(t) y. L-1 ymax Transmit Iin(t) y. L 0 LT 2 LT t y 0 ymin y-1 t 0 -(L+1)T t 0 -LT t 0 -T t 0 t 49

Estimation of the Objective Function g(t) g(n. T; t 0) 0 T 2 T 3 T 4 T 5 T 6 T t - t 0 Eye open: transmit data sequence Receive y(t) = Iout(t) * r(t) Transmit Iin(t) y 0 y 1 t Fˆ (g (n. T ; t 0 ))= y 1 - y 0 t (mod T) 50

Experimental Results: 10 Gbps 51

Experimental Results: 10 Gbps 4 mm offset patch cord, 2 km fiber Before Adaptation After Adaptation 52

Experimental Results: 10 Gbps 4 mm offset patch cord, 2 km fiber Power Scan 53

Experimental Results: 10 Gbps 4 mm offset patch cord, 2 km fiber Channel Scan Channel spacing: 50 GHz Channels 54 -59 error free. 300 GHz at 50 GHz spacing. 54

Experimental Results: 10 Gbps 2 mm offset patch cord – 500 m fiber – 2 mm offset patch cord – 500 m fiber Before Adaptation After Adaptation 55

Experimental Results: 10 Gbps 56

Experimental Results: 10 Gbps 57

Experimental Results: 100 Gbps, 2. 2 km 58

Experimental Results: 100 Gbps, 2. 2 km Pilot. BER-based channel-based adaptation Corning Incorporated: Infini. Cor e. SX+ fibers R. A. Panicker, J. P. Wilde, J. M. Kahn, D. F. Welch and I. Lyubomirsky, IEEE Photon. Technol. Lett. , vol. 19, no. 15, pp. 1154 -1156, August 1, 2007. 59

Experimental Results: 100 Gbps, 2. 2 km FEC Decoder Input BER Power in 0. 2 nm BW (d. Bm) 100 10 -2 FEC Threshold 10 -4 10 -6 10 -8 -5 10 -10 0 -10 1 2 3 4 5 6 7 8 9 Attenuator Setting (d. B) -15 -20 -25 1549 1553 1557 1561 1565 Wavelength (nm) 60 10

Experimental Results: 100 Gbps, 2. 2 km FEC Decoder Input BER Power in 0. 2 nm BW (d. Bm) 100 10 -2 FEC Threshold 10 -4 10 -6 10 -8 10 -100 -5 1 2 3 4 5 6 7 8 9 Attenuator Setting (d. B) -10 -15 -20 -25 1549 1553 1557 1561 1565 Wavelength (nm) 61 10

Experimental Results: 100 Gbps, 2. 2 km 62

A Subtlety l l Exciting a single principal mode is not the best way to maximize the eye opening! Allow some higher order modes to be excited. Additional power in desired mode more than compensates. A non-intuitive outcome of the optimization framework. 63

A Subtlety 64

Conclusions Adaptive optics can effectively compensate for modal dispersion even in presence of real-world impairments. l An optimization framework can be used to compute the globally optimal solution. l These techniques have been successfully used for 10 Gbps and 100 Gbps transmission over multiple kilometers with channel impairments. l 65

Thank you 66

Acknowledgements Prof. Joseph Kahn l Prof. Stephen Boyd l Prof. Shanhui Fan l Prof. Balaji Prabhakar l 67

Acknowledgements l Members of the group 68

Acknowledgements l Dr. Martin Lee 69

Acknowledgements l Family 70

Acknowledgements l Namita and Gaurav 71

Acknowledgements Shravan l Dev l 72

Acknowledgements l Many more friends 73

Adaptive Optics Subsystem 74

Transmitter and Receiver Components l Laser Iolon MEMS-based tunable laser l C band (1527 -1567 nm), 100 channels on 50 GHz ITU grid l +13 d. Bm output power, 15 k. Hz linewidth (not required here) Modulator l Fujitsu 12. 5 Gb/s dual-drive Mach-Zehnder modulator, zero chirp l Encodes 10 Gb/s on-off keying, non-return-to-zero format Receiver l Picometrix 12. 5 Gb/s receiver, 62. 5 mm MMF input l Sensitivity and overload powers: -20 d. Bm, + 2 d. Bm at 10 -10 BER Average powers l Modulator output: +6 d. Bm 75 l Launched into MMF: -2. 5 d. Bm l Receiver input: -3. 4 d. Bm (1 km) to -5. 5 d. Bm (11 km) l l

Estimation of ISI Objective Function g(t) g(n. T; t 0) 0 T 2 T 3 T 4 T 5 T 6 T t - t 0 Eye closed: transmit periodic square wave Receive y(t) = Iout(t) * r(t) y. L-1 ymax Transmit Iin(t) y. L 0 LT 2 LT t y 0 ymin y-1 t 0 -(L+1)T t 0 -LT t 0 -T t 0 t 76

Convergence Time l Bit rate on feedback channel: 8 bits/135 ms = 59 kb/s. l 128 bit training sequence, measure 6 points, average 2000 measurements. Estimation accuracy required: F/s. F = 256 (8 bits). In absence of ISI, Q = 7. 1 km link length, 10 Gb/s. 77 l l l

Nematic Liquid Crystal SLM l Made by Boulder Nonlinear Systems l Pixels: 256 × 256 l Nematic liquid crystal, phase only l Phase range: 0 to 2 p l Resolution: 5 -6 bits l Reflection efficiency: 65% l Response time l l Binary {p, 2 p}: t 10 -90 50 ms l Quaternary {p/2, p, 3 p/2, 2 p}: t 10 -90 100 ms Polarization-sensitive l Not suitable for receiver in MIMO system 78